SOLUTION: Prove that the set of all 3 x 3 matrices with real entries of the form [ 1 a b 0 1 c 0 0 1] is a group. (Multiplication is defined by [ 1 a b

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Question 95450This question is from textbook
: Prove that the set of all 3 x 3 matrices with real entries of the form
[ 1 a b
0 1 c
0 0 1]

is a group.
(Multiplication is defined by [ 1 a b
0 1 c
0 0 1] x
[1 a' b'
0 1 c'
0 0 1]

[ 1 (a+a') (b'+ac'+b
0 1 c'+c
= 0 0 1 ]
this group, sometimes called the Heisenberg group after the Nobel Prize winning physcicist Werner Heisenberg, is intimately related to the Heisenberg Uncertainty Principle of quantum physics. )
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This question is from textbook

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